Aces are high. If trumps exist, they are strictly higher than nontrump cards. The object of the basic game is to win the most turns (sometimes called "tricks").
For the basic game, the entire deck is dealt out and play begins with the player on the dealer's left.
Each player (in order, clockwise from the first player) plays one card.
The cards are then compared, and the player who played the highest card wins the turn. In the basic game, they keep all the cards played that turn so they can keep track of how many turns they won.
Play then passes to the left (that is, the person to the first player's left will be the first player next turn).
The basic game ends when everyone runs out of cards.
Multiple rounds are played (as above) - with the starting hand size decreased by one each round. The winner of a round chooses trumps (after looking at their hand) for the next round. The winner is then the one who wins most rounds.
Contract Whist (aka "Solo")
Forget bridge and all its awful complexities - this is whist with even more complexities.
Also known as solo whist, despite being a four person game.
One card is turned face up, designating trumps.
Similarly to contract bridge, layers play in teams and bid against each other, hoever the bidding differs:
The lowest bid is 'proposal' - this is equivalent to a bridge bid of 'two' (ie. eight tricks) - in the suit of the face up card. However - it is NOT a contract with the person sitting opposite you, ANY person around the table can accept your proposal and (unless overbid) you end up in partnership with them. There's also none of this 'sit out for a round' rubbish with dummy :)
The next highest bid is solo - which is a -1 contract with NO partner - you against the other three, but you only have to take five tricks. Again, trumps are as dealt.
Misere is the next bid, meaning that you have such a bad hand you will take NO tricks. With this bid, there are no trumps.
Erm, it's worth pointing out that a Misere hand is in no way considered "bad"; and if played compettively would probably take a fair few tricks. As anyone who has spent too long playing Hearts will know. --SF
Abondance (sometimes called Abundance by silly^Hanglicised players/books) is a solo call, but with a contract of 3 (ie. will take nine tricks) - but you get to choose trumps (AFTER everyone else has passed the bidding)
Abondance in trumps is the same, but means that you accept the trump suit that has been turned face up.
Misere Ouverte (or "Open Misere" when anglicised) is like Misere, but outbids Abundance because the Misere bidder lays their hand face up and the other players may then conspire to look for a way to force her to take a trick.
This is highly amusing, although StuartFraser has still only seen it once in a great many hands of the game.
The highest bid is Abondance Declarée, and means "Bidding ends here. There are no trumps. I will lead and win every trick. There's nothing you can do to stop me nah nah na nah nah."
Otherwise, basically bridge (ie. plays like whist), but with easier bidding and fewer numbers to keep track of. (A won hand is a won hand, none of this overtrick stuff)
Vitenka would like to chip in here and say that solo contains almost all of the complexity and enjoyment of contract (rubber) bridge. It really is fun - although it's worth noting that bids above abondance (in trumps, if you happen to be lucky enough to get that suit) are incredibly rare.
There are specific shuffling techniques designed to make the rarer hands more likely. Basically, after a hand in which no contract is made, cards are placed in your hands in a specific order, put on top of each other, and dealt out in clumps. --Angoel
Played with two players. "It's a game of two halves", each of which consists of 13 two-person tricks of whist.
Setup: deal each player 13 cards. The remaining 26 form the deck.
First half: these 13 tricks are played no-trumps. Before each trick, turn the top card of the deck face-up. Whoever wins this trick gets that card into their hand. The other player gets the next, unknown, card from the deck into their hand. Thus hand size stays constant at 13 for the first half.
Second half: whoever won more tricks in the first half gets to choose trumps. Then you play out your hands against each other. Winner is the player who's won the most total tricks between the two halves. 13-13 draws are possible, and happen occasionally.
Strategy: The first half is a nice balance between trying to accumulate a long suit, accumulate power cards for the second half, and get to the magic 7 tricks in order to actually choose this long suit as trumps for the second half.
A game for two players
Setup: Deal each player 20 cards in four rows of five cards each. The second and fourth (fourth being uppermost) rows are face-up, the third and first face down. The remaining 12 cards are dealt into a six-card hand for each player.
Play: Twenty-six tricks are played; players may play cards from either their hands or whatever face-up cards they have on the table. When a face-down card becomes the next card in that column, it is turned face up. The winner is the player who takes the most tricks.
Strategy: Based almost entirely around the suprise factor of cards in your hand (which you know about but your opponent does not) and the face-down cards you have on your table (which neither of you know about). Produces somewhat similar feelings to playing MtG with/against lots of morphs, for those of you who've done that.